Singing is a human capacity that seems absolutely natural and even constitutive of our humanity. Nothing could be more affectingly human than the imagined scene of a mother or father singing a child to sleep, or a child waking up singing to itself in the morning. An inability to sing is experienced as isolating, and those who claim that they just can't hold a tune seem to think of it as a great sadness.

Any worthwhile vocal cheerleader – Gareth Malone from the TV programmes The Choir and Military Wives is the latest, excellent example – will tell the terrified and tuneless that, actually, anyone can sing. Apart from the impediments of age or physical disability, the essentially psychological blocks that constitute being, in the loose and commonplace sense, "tone deaf" can be coaxed away.

John Potter is a distinguished singer (a longstanding participant in the English early music scene as a member of the Hilliard Ensemble and Red Byrd) and sometime academic; his co-author, Neil Sorrell, is a scholar of Indian and Javanese music, co-founder of the English Gamelan Orchestra. Their fascinating and dense book A History of Singing reminds us – one might expect as much from writers of such diverse backgrounds – of the disorientating variety of song traditions in human cultures, historically and geographically. Singing may seem to be a simple, natural ability, but it is always mediated by culture; the authors quote the French ethnomusicologist François-Bernard Mâche's account of the Toraja of Sulawesi (in Indonesia) who have no lullabies, wedding songs or dirges and "never make music for the sole pleasure of singing or listening" but only as a matter of ceremony.

Potter and Sorrell's first chapter, "Origins, Myths and Muses" comes up against the central problem of any historical account of singing: almost all of the evidence, written in the air, has dispersed. We know that the human vocal tract has been around for millions of years, but we're not even sure how or why it evolved – to make swallowing safer, or to aid human communication, or both. We can tell the sort of just-so stories favoured by the evolutionary psychologists, but Rudyard Kipling's originals often seem just as much evidence-based and a good deal more entrancing (my favourite account of singing in the mists of time is the Woman in "The Cat that Walked by Himself", who makes the first singing magic). "No genetic imperative for singing has been discovered in human beings," we are told, "although highly structured sounds are produced by members of every society." Highly structured sounds are one thing, singing another, though whether Potter and Sorrell's careful definition of singing – "a tuneful and pleasant vocalisation of discrete pitches" – will stretch to accommodate Lotte Lenya, Bob Dylan or Lou Reed is a moot point.

Once the historical record starts, of course, we have indirect evidence of what singing in western Europe was – increasing amounts of it, although it remains hard to interpret. Treatises on singing, for example, are often written by less successful singers, those with an agenda about declining taste or professional opportunities. Potter and Sorrell are imaginative and acute with sometimes fugitive evidence, pointing to the pictures of huddled monks singing to suggest that the relish for resonance that we associate with church singing (and singing in the shower) is not necessarily universal.

Once a way had been found to write music down – a "technology" which developed out of the medieval monastery, with its imprecise neumes, and achieved a new beginning with the staff notation associated with the 11th-century Italian, Guido of Arezzo, which we still use – a conflict was implicit between music as performance and music as text. A treatise De Musica dating from about 1100 captures brilliantly the way in which practical music-making could stray from the nostrums of the theorists and those who wrote music down: "To whom then should I better compare the singer than to a drunken man who does indeed get home but does not in the least know by what path he returns?"

By the beginning of the 17th century, and the birth of opera, the solo singer was likely to be a virtuoso who embroidered on the musical structure provided by the composer. In some ways these performers were more like jazz singers than the academically trained vocalists and humble interpreters of the early 21st century.

For most of the period we know much about, the singer was in the ascendant. Take the 18th-century divo, Carlo Maria Michelangelo Nicola Broschi, better known as the castrato Farinelli. It was the great Farinelli whom people came to hear, it was Farinelli who in a very real sense owned the music he was given to sing. He earned a fortune. For more than 20 years he lived as an influential courtier in Bourbon Madrid, dying in Bologna in 1782 with a substantial estate that included paintings by Murillo, De Ribera and Velàzquez. The greatest composer who wrote for Farinelli, George Frideric Handel, despite being a genius was, by comparison, unacknowledged. Farinelli even wrote music himself …

The 19th century saw a shift from "creative virtuosity" to "interpretative artistry", but it happened by fits and starts. If Rossini tried to keep a rein on his singers by providing them with the cascades and roulades they wanted (while at the same time hating the new high notes, the robust top Cs, which have defined the popular idea of a tenor ever since), Verdi still struggled to get singers to sing what he had actually written. It's fascinating to realise that while the German Wagner was obsessed with singers and singing, with an ideal of "bel canto", it was the Italian, Verdi, who had little interest in singing for its own sake.

The book ends with a fervent sense that somehow the limitations and boundaries that the history of classical music has imposed on singers can now be transcended. In the 20th century both recording technology, and the primacy of the composer in classical music, opened up a gulf between popular and classical singing which has been difficult to bridge. The "plurality of singings", which the authors suggest as an alternative, is all very well, but I remain convinced, in the end, that the seriousness of purpose which, over the centuries, the classical music tradition has developed and accumulated, will stand it in good stead.